ESAT Maths 1 · free worked solution

ESAT Maths 1 trigonometry: find cos θ

Trigonometry solution: use Pythagoras first, then identify adjacent over hypotenuse for 12/13.

Right-triangle trigonometrySpecification M5.18Reviewed 9 August 2026

Answer first

Option B

The correct answer is

$\frac{12}{13}$

The cable is the hypotenuse; the horizontal ground distance is adjacent to the requested angle.

This is original UniGenius practice material from the reviewed Maths 1 bank. It is not an official UAT-UK question, past paper, or recalled question.

The question

Read the setup, then choose the shortest valid route

A cable is $13\,\mathrm{m}$ long and joins a point on the ground to a point $5.0\,\mathrm{m}$ above the ground. What is the cosine of the angle the cable makes with the ground?

A $\frac{5}{13}$
B $\frac{12}{13}$ Answer
C $\frac{5}{12}$
D $\frac{12}{5}$
E $\frac{13}{12}$

Worked solution

The route in 4 steps

Pythagoras gives the horizontal side as $\sqrt{13^2-5^2}=12\,\mathrm{m}$ .
The horizontal side is adjacent to the ground angle, while the cable is the hypotenuse.
For the angle with the ground, the horizontal side is adjacent and the cable is the hypotenuse, so use the cosine relationship.
The required value is $\cos\theta=12/13$ .

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